Building a Better World Series
Why the Fall Classic isn't the best way to find the best team in baseball.
Red Sox 4-0 9.2 percent
Red Sox 4-1 16.5 percent
Red Sox 4-2 18.5 percent
Red Sox 4-3 16.7 percent
Cards 4-3 13.6 percent
Cards 4-2 12.4 percent
Cards 4-1 9 percent
Cards 4-0 4.1 percent
So, the better team, the Red Sox, will win 60.8 percent of the time. The Series has a 13.3 percent chance of ending in 4 games; the chance that it goes 5, 6, or 7 games is 25.5 percent, 30.9 percent, and 30.3 percent respectively. So, the expected length of the real World Series is
4 x .133 + 5 x .255 + 6 x .309 + 7 x .303
or 5.78 games. The corresponding numbers for the Alternate World Series are a 61.4 percent chance that the better team will win, with an expected length of 5.72 games. And the AWS isn't just better when we arbitrarily set p equal to .55. The AWS is both shorter and more accurate than the real World Series if one of the teams has a 60 percent chance or a 65 percent chance of winning each game. In fact, the AWS is better on both criteria for whatever reasonable value we choose for p. (I say "reasonable" because this statement fails when p is close to 0 or 1, e.g., if one team has only a 5 percent chance of beating the other in each game. It seems safe to say that there's never been a World Series in which the teams were this badly mismatched.)
The Alternate World Series has some other appealing features besides its efficiency and accuracy. Unlike the best-of-seven model, but like tennis, a team at the brink of elimination can buy itself some breathing room with a win. One potential problem with the new system is that it might give an advantage to teams with two powerful starters who could dominate the first two games, giving them the chance to close out the Series in three games without ever exposing the weakest part of its starting rotation. On the other hand, a series that goes to eight or nine games might reward a team with a deeper pitching staff.
Tradition has a value of its own, so I couldn't blame baseball for sticking with the tried-and-true World Series format despite the advantages of the AWS. But maybe another league, perhaps one that has already changed playoff systems a few times and is desperately in need of some positive PR, would be willing to try something new. Stanley Cup Finals Game 9, here we come!
Jordan Ellenberg is a professor of mathematics at the University of Wisconsin. His book How Not To Be Wrong is forthcoming. He blogs at Quomodocumque.